       + 37k123k1232
(k1k23)(k1k23)k12k232
[1 - (k2 k3k2 k3)2],


where \({k}_{12}={k}_1+{k}_2\) ,
\({k}_{123}={k}_1+{k}_2+{k}_3\) , and \(+\,\mathrm {cyc.}\) 
corresponds to the two terms which are added with cyclic permutations
of each previous term. Weak dependences on the time in the kernels
are neglected [1]}, [2]}. In
Ref. [2]}, complete expressions of the
displacement kernels of LPT up to the seventh order including the
transverse parts are explicitly given, together with a general way of
recursively deriving the kernels including weak dependences on the
time in general cosmology and subleading growing modes. The
redshift-space distortions can be simply taken into account as well in
the Lagrangian perturbation theory, just replacing the displacement
kernel in real space given above with the linearly mapped kernels
[4]}
\({L}_n \rightarrow {L}^\mathrm {s}_n = {L}_n +nf\left(\hat{{z}}\cdot {L}_n\right)\hat{{z}},\) 
